Colin Kazim-Richards' second-half strike earned Rovers a 1-0 weekend win at the Emirates Stadium. An away quarter-final tie against Millwall is their reward and Appleton's squad return to league action at Hull on Tuesday night having been told they experienced a career highlight on Saturday.
"I think if you look back on recent stats, not just Blackburn versus Arsenal, Arsenal against any team at any level at the Emirates in cup competitions and we could stay here for ages and talk about how many times they've turned over teams by five or six goals in recent season," Appleton said.
"They'd never lost an FA Cup tie at the Emirates. I can't remember the last time Blackburn kept a clean sheet away to Arsenal.
"So if you put all the facts and stats together it's one hell of an achievement. I said to the players after the game, 'don't play down what an achievement, what a performance and a result this has been today because it's as good as you'll ever get in your career'."
Hull head into the match occupying the second automatic promotion spot. While such ambitions appear beyond Blackburn following a tumultuous season on and off the pitch, an upturn in fortunes and an air of much-needed stability established since Appleton's arrival last month mean a play-off place is a realistic proposition.
"Since I walked into the football club I've tried to improve the mentality of the players on a day-to-day basis and going into the games, making sure we're harder to beat and respecting the division because we've got a few players who've played at a higher level for quite some time," said the former Portsmouth and Blackpool boss.
"I also want to make sure there's normality about the football club and everyone not associated with the football club is talking about football because, ultimately, that's what we get paid to do.
"The results count for a lot of things, but if the players know that when they come into the football club they're going to go into an environment where it's stable and it's nice to work at, then they're going to produce their best football.
"I have a points target myself but it's not a discussion that I've had with the players. I want the players to be focusing on the mentality of trying to win every game."